NEW YORK, Sept 27 (Reuters) - The U.S. dollar held near a one-week high against a basket of major currencies on Thursday following an interest rise by the Federal Reserve on Wednesday, while robust economic growth and a rally in the shares of Apple Inc and Amazon.com Inc boosted the U.S. stock market.

The Fed on Wednesday raised rates for the third time this year, indicating its confidence in the U.S. economy.

That sentiment carried the U.S. dollar higher into a second day and dented the euro, which was further pressured by worries about Italy's budget deficit.

"The Fed is moving faster than most central banks and that's dollar-supportive," said Erik Nelson, currency strategist, at Wells Fargo Securities in New York.

The dollar index rose 0.85 percent, with the euro down 0.83 percent to $1.1641.

The greenback also hit a four-week peak against the Swiss franc and a two-week high versus the Canadian dollar .

The Dow Jones Industrial Average rose 54.65 points, or 0.21 percent, to 26,439.93, the S&P 500 gained 8.03 points, or 0.28 percent, to 2,914 and the Nasdaq Composite added 51.60 points, or 0.65 percent, to 8,041.97.

Apple rose 2.5 percent at one point, the biggest boost to the three main U.S. stock indexes after JP Morgan re-started coverage of the stock with an "overweight" rating.

"The Fed's statement is essentially a green light for the economy. It's a confirmation that the U.S. economy is the best game in town for global investors," said Jeffrey Kravetz, regional investment director at the Private Client Reserve of U.S. Bank.

Adding to positive sentiment was data showing U.S. economic growth accelerated in the second quarter at its fastest pace in nearly four years as previously estimated.

ITALY

Italy's main Milan bourse slumped as much as 2.0 percent , closing down 0.6 percent, with the country's big banks sinking even more as the country's borrowing costs hit a three-week high in the government bond markets.

Later Thursday Italy's government agreed to target next year's budget deficit at 2.4 percent of gross domestic product, party chiefs said, ending a tussle between the ruling parties and Economy Minister Giovanni Tria.

The move is a concession by Tria, who had wanted a deficit set as low as 1.6 percent, and appears at odds with Italy's promise to the European Union that it would cut the deficit decisively to rein in its high debt.

Italian asset prices may come under pressure on Friday, as financial markets had been betting on Tria to resist the spending push from Salvini and Di Maio, who are both deputy prime ministers.

"The good news is that there is a deal, at last," said Francesco Galietti, head of Rome-based political risk consultancy Policy Sonar. "The more complex part, however, is that until today markets had been betting on Tria's capacity to rein in political forces. That assumption is now crumbling."

There was no immediate word from Tria, but government sources said he had no intention of resigning.

"From now on things will be tough for Italy," said Armando Marozzi, analyst at Medley Global Advisors. "The European Commission will reject this budget and next month ratings agencies are likely to downgrade Italian bonds."

Japan's Nikkei touched an eight-month high as signs that the United States may not impose further tariffs on Japanese automotive products for now lifted carmakers, though the index eventually ended down nearly 1 percent.

Benchmark 10-year Treasury notes last rose 2/32 in price to yield 3.0536 percent, from 3.061 percent late on Wednesday.